von Neumann’s biased coin revisited

Laurent Bienvenu 1 Benoit Monin 2
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Suppose you want to generate a random sequence of zeros and ones and all you have at your disposal is a coin which you suspect to be biased (but do not know the bias). Can "perfect" randomness be produced with this coin? The answer is positive, thanks to a little trick discovered by von Neumann. In this paper, we investigate a generalization of this question: if we have access to a source of bits produced according to some probability measure µ in some class C of measures, and suppose we know C but not µ (in the above example, C would be the class of all Bernoulli measures), can perfect randomness be produced? We will look at this question from the viewpoint of constructive mathematics and in particular the theory of effective randomness.
Document type :
Conference papers
Liste complète des métadonnées

Cited literature [10 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01397207
Contributor : Benoit Monin <>
Submitted on : Tuesday, November 15, 2016 - 3:38:33 PM
Last modification on : Wednesday, December 19, 2018 - 3:50:03 PM
Document(s) archivé(s) le : Thursday, March 16, 2017 - 4:35:23 PM

File

paper_biased_coin.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01397207, version 1

Citation

Laurent Bienvenu, Benoit Monin. von Neumann’s biased coin revisited. LICS: Logic in Computer Science, Jun 2012, Dubrovnik, Croatia. 2012. 〈hal-01397207〉

Share

Metrics

Record views

248

Files downloads

56